Planetary Gears: How to rig for rigid body physics engine?
You have already done the most part of the job.


Connect the gray cylinder (the bottom one) to each of the pink cylinder with a constraint of type hinge.
The created empties (empties added by the previous constraints) need to be aligned on the center of the system (Z axis) as the pink cylinders need to rotate around this axis
Set all the pink cylinders to active as they need to move
Set the yellow gear to passive as it needs to stay in place